A random variable X assumes values 1, 2, 3, l | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The probability distribution is given by the table:| $X=x$ | $1$ | $2$ | $3$ | $\ldots$ | $n$ ||---|---|---|---|---|---|| $P(X=x)$ | $\frac{1}{n}$

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(C) The probability distribution is given by the table:| $X=x$ | $1$ | $2$ | $3$ | $\ldots$ | $n$ ||---|---|---|---|---|---|| $P(X=x)$ | $\frac{1}{n}$ | $\frac{1}{n}$ | $\frac{1}{n}$ | $\ldots$ | $\frac{1}{n}$ |$E(X) = \sum x P(X=x) = \frac{1}{n} (1 + 2 + \ldots + n) = \frac{1}{n} \cdot \frac{n(n+1)}{2} = \frac{n+1}{2}$$E(X^2) = \sum x^2 P(X=x) = \frac{1}{n} (1^2 + 2^2 + \ldots + n^2) = \frac{1}{n} \cdot \frac{n(n+1)(2n+1)}{6} = \frac{(n+1)(2n+1)}{6}$$\operatorname{Var}(X) = E(X^2) - [E(X)]^2 = \frac{(n+1)(2n+1)}{6} - \left(\frac{n+1}{2}\right)^2$$= \frac{(n+1)}{2} \left[ \frac{2n+1}{3} - \frac{n+1}{2} \right] = \frac{(n+1)}{2} \left[ \frac{4n+2 - 3n - 3}{6} \right] = \frac{(n+1)(n-1)}{12} = \frac{n^2-1}{12}$Given $\frac{\operatorname{Var}(X)}{E(X)} = \frac{4}{1}$,we have:$\frac{(n^2-1)/12}{(n+1)/2} = 4$$\frac{(n+1)(n-1)}{12} \cdot \frac{2}{n+1} = 4$$\frac{n-1}{6} = 4$$n-1 = 24$$n = 25$

$A$ random variable $X$ assumes values $1, 2, 3, \ldots, n$ with equal probabilities. If $\operatorname{var}(X) : E(X) = 4 : 1$,then $n$ is equal to

Similar Questions

Two dice are rolled. If a random variable $X$ denotes the sum of the numbers on them and $\mu$ denotes the mean of $X$, then $\mu+P(X < 5)+P(X>9)+P(X=7)=$

If $3$ is the variance of a Poisson distribution,then $P(1 < x < 4) = $

$A$ fair $n$-faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$,then $n=$ (where $n \in N$ ).

If $P(X = x) = 5r^x$, $x = 1, 2, 3, \dots$ is the probability mass function of a discrete random variable $X$, then $r = $

$A$ fair die is tossed twice in succession. If $X$ denotes the number of fours in $2$ tosses,then the probability distribution of $X$ is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module